They said the body of James Henry, 55, who told authorities he was a retired officer, was found at noon at Ismailiya Awal police station.
Henry had been detained in August for violating a curfew imposed because of the latest wave of political unrest sweeping Egypt.
He was stopped on the road between El-Arish and Rafah in North Sinai and told authorities he was on his way to the Gaza Strip.
Officials said that a US embassy delegation had visited Henry in his cell last week.